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Evaluate the definite integral. $ \displaystyl…
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Problem 55 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^1_0 \sqrt[3]{1 + 7x} \, dx $

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01:36

Frank Lin

Related Courses

Calculus 1 / AB
Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

Related Topics

Integrals

Integration

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Integrals - Intro

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
Video Thumbnail

40:35
Area Under Curves - Overview

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
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Watch More Solved Questions in Chapter 5

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Problem 7
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Problem 16
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Problem 28
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Problem 71
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Problem 76
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Problem 78
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Problem 81
Problem 82
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Problem 85
Problem 86
Problem 87
Problem 88
Problem 89
Problem 90
Problem 91
Problem 92
Problem 93
Problem 94

Video Transcript

1.7 Next to the 1/3 DX and I were looking at the integral from 01 We know we can divine are you? And then we can define our d acts. VX is do you over seven. Given this, we can now write or integral in terms of you. And now the upper limit is going to be you is one plus sometimes one, which is eight. So we now have the integral from 1 to 8. Okay, let's pull up the constant, which is 1/7. Yeah, and now we know that we can use the power rule which is increased the expert it by one and divide by the new exponents. And now we're climb a fundamental theme of calculus by plugging end our bounds to get 45 over 28.

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Top Calculus 1 / AB Educators
Grace He

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Lectures

Video Thumbnail

05:53
Integrals - Intro

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
Video Thumbnail

40:35
Area Under Curves - Overview

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
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Evaluate the definite integral. $\int_{0}^{1} \sqrt[3]{1+7 x} d x$

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Evaluate the definite integral. $$\int_{0}^{1} \sqrt[3]{1+7 x} d x$$

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